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  • Characterization of GLONASS Broadcast Clock

    and Ephemeris: Nominal Performance and Fault

    Trends for ARAIM Kazuma Gunning, Stanford University

    Todd Walter, Stanford University

    Per Enge, Stanford University


    Kaz Gunning is a Ph.D. candidate in the GPS Research Laboratory working under the guidance of Professor Per Enge and Dr.

    Todd Walter in the Department of Aeronautics and Astronautics at Stanford University. Prior to joining the lab in fall 2015 as

    a Ph.D. candidate, Kaz worked for Booz Allen Hamilton on the GPS Systems Engineering and Integration group doing

    Modeling and Simulation of the next generation GPS Control Segment and software-defined receiver work looking at the GPS

    III waveform. His interests are in GNSS modernization and integrity.

    Todd Walter is a senior research engineer in the GPS Research Laboratory in the Department of Aeronautics and Astronautics

    at Stanford University. He received his Ph.D. from Stanford in 1993 and has worked extensively on the Wide Area

    Augmentation System (WAAS). He is currently working on dual-frequency, multi-constellation solutions for aircraft guidance.

    He received the Thurlow and Kepler awards from the ION. In addition, he is a fellow of the ION and has served as its president.

    Per Enge is a Professor of Aeronautics and Astronautics at Stanford University, where he is the Vance and Arlene Coffman

    Professor in the School of Engineering. Here, he directs the GPS Research Laboratory which develops navigation systems

    based on the Global Positioning System (GPS). He has been involved in the development of WAAS and LAAS for the Federal

    Aviation Administration (FAA). He has received the Kepler, Thurlow, and Burka Awards from the ION. He also received the

    Summerfield Award from the American Institute of Aeronautics and Astronautics (AIAA) as well as the Michael Richey Medal

    from the Royal Institute of Navigation. He is a fellow of the Institute of Electrical and Electronics Engineers (IEEE), a fellow

    of the ION, a member of the National Academy of Engineering, and has been inducted into the Air Force GPS Hall of Fame.

    He received his Ph.D. from the University of Illinois in 1983.


    This paper characterizes the GLONASS broadcast clock and ephemeris performance over an eight year period from 2009

    through 2016, where both nominal signal-in-space (SIS) user range error (URE) and faulty behavior are explored. While GPS

    is currently widely used in aviation via receiver autonomous integrity monitoring (RAIM), advanced RAIM (ARAIM) could

    allow for a multi-GNSS navigation solution that potentially includes GLONASS. In order to demonstrate the safety of such a

    system, the performance of each GNSS must be carefully evaluated.

    GLONASS broadcast clock and ephemeris parameters are evaluated through comparison with precise clock and ephemeris

    products provided by the International GNSS Service (IGS). Clock and ephemeris error are combined to produce SIS URE

    values and compared against fault criteria. More than 300 faults over the last eight years have been identified and categorized

    by whether they are faults in clock and/or ephemeris, the health state of the satellite preceding the fault event, the duration of

    the fault, and other criteria. The data shows a significant improvement in fault rate and duration, where several classes of faults

    that were once relatively common have not been observed in several years. Additionally, due to limited GLONASS monitoring

    and upload stations, a geographic correlation with fault events is observed. This paper estimates the probability of independent

    satellite faults, Psat, and probability of simultaneous satellite failures, Pconst, over this period. Nominal SIS URE performance

    is also examined, where SIS ranging biases and error distributions are assessed for each satellite for both clock and ephemeris.

    The analysis shows nominal ranging accuracy improvement since 2009 in both clock and ephemeris.



    The use of ARAIM requires knowledge of the performance of each of the constellations used. In particular, the signal in space

    user range error distribution is modeled as a Gaussian with some probability of exceeding a threshold, over which a major

    service failure or fault is declared. Historical data can be used to evaluate whether or not each GNSS has met the commitments

    that have been made towards performance both in nominal behavior and faulted behavior. GLONASS is of particular interest

    because it is currently the only fully operational GNSS outside of GPS, as it has had a full 24-satellite constellation in operation

    since 2010, as shown in Figure 1. Ranging performance has been quantified and estimates of Psat, Pconst, and nominal error

    distributions have been produced for GPS [1] in the past. Initial studies of Galileo performance alongside GPS have been

    produced [2] as well as multi-constellation nominal performance studies [3]. To an extent, GLONASS performance has also

    been investigated though the identification of faults and a description nominal ranging accuracy performance through the period

    2009 to 2012 by Heng [4, 5].

    The goals of this paper are two-fold: to characterize the fault rate over time of the GLONASS constellation and to characterize

    the nominal error distribution over the period of 2009 to 2016. The error of interest is the error related to signal transmission;

    terrestrial and receiver effects are not considered. The error studied comes from the constellation service providers (CSP)

    estimation of the satellite clock and ephemeris state as broadcast in the navigation message. This paper uses historical data to

    determine the signal-in-space (SIS) user range error (URE) distribution- the distribution of the error contribution from the

    satellite and CSP on the ranging signal as observed by a terrestrial user.

    Figure 1: GLONASS Constellation Progression- Number of satellites by block and mean age of active satellites over time

    Fault threshold

    A draft of the GLONASS performance specification has stated that a GLONASS fault is declared when the SIS URE exceeds

    70 meters, and the commitment is to a probability of such an event, Psat, of 10-4 [6]. Similarly, the commitment to the probability

    of a constellation-wide fault, Pconst, is 10-4. For a Gaussian error distribution, a 70 meter event at the 10-4 level corresponds to

    a standard deviation of approximately 18 meters. This fault threshold and Psat commitment thus sets a floor for the ranging

    error standard deviation of 18 meters. This study uses the 70 meter fault criteria and, when applicable, a URA of 18 meters.


    The primary mode of analysis in this study is the comparison of the estimated satellite clock and ephemeris as broadcast by the

    navigation message to the precise estimates of the satellite clock and ephemeris produced by various analysis centers (AC). At

    each epoch, the broadcast clock and ephemeris are differenced with the precise clock and ephemeris, and the position error is

    rotated to the satellite local radial, along-track, and cross-track frame. The error is also projected onto the line of sight of a grid

    of 200 evenly spaced users across the globe in order to better capture the user range error for all users. Many metrics only

  • consider the average URE across the globe, but for high integrity applications, we are concerned with protecting the worst case

    user as well. The broadcast navigation messages are logged by the International GNSS Service (IGS) [7] receiver network.

    All of the navigation message logs are downloaded and combined using a voting method as described by Heng [8]. Voting

    between the logged navigation message logs is performed in order to screen out erroneous navigation message logs.

    Unfortunately, the RINEX navigation message files do not have a field for FT, the GLONASS equivalent of the GPS URA

    term. In the future, if the fault threshold is changed to be a function of FT, then a separate source of historical FT values will be

    required for further analysis.

    The precise clock and ephemeris estimates used in this study come from the Information Analytical Center of GLONASS

    (IAC), which is an AC and contributor to the IGS final GLONASS ephemeris solution. The IGS final solution is not utilized

    in this study because it does not include clock estimates. The error in the IAC clock and ephemeris solution is limited to

  • The ionosphere-free pseudorange measurement can be modeled as

    = + + + (2) where r is the true range, c is the speed of light, bu is receiver clock bias, bs is the true satellite clock bias, T is the tropospheric

    delay, and is made up of all additional unmodeled effects, modeling errors, and measurement noise. Clock and ephemeris error can be represented as

    = (3) = !" (4)

    where #%&'()* is the range computed using broadcast ephemeris, +,) %&'()* is satellite clock bias computed using broadcast clock parameters, and -./01 and 23-24are the range errors from the broadcast orbit and broadcast clock error, respectively. Signal-in-space user range error can then be computed:

    565 6789 = !" (5) 565 6789 = + : ; + + (6)

    For a static receiver at a known location, ionosphere-free measurements from the satellite of interest, and a tropospheric delay

    model, the only remaining term to f